In these lectures I'll try to give a whirlwind tour of this fascinating subject, stopping to smell at least some of the roses. I will also state a number of open problems along the way.

In lecture II I'll describe Teichmuller space and the moduli space of Riemann surfaces, and we'll see how the mapping class group plays a central role. I'll describe a universal property of moduli space. Then I'll explain Bers's proof of the Thurston classification of surface homeomorphisms, which uses Teichmuller geometry. It is a paradigm for a whole way of thinking

Lecture #12547

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